1. BEATRICES 
1.1 Introduction 
1.2 Some types of matrices 
1.3. Equal matrices 
1.4. Matrix addition 
1.5. Scalar multiplication 
1.6. Transpose of a matrix 
1.7. Symmetric and skew-symmetric matrices 
1.8. Matrix multiplication 
1.9. The trace of a square matrix 
1.10. Exercises 
1.11. Answers

2. DETERMINANTS 
2.1. Introduction 
2.2. Properties of determinants 
2.3. Exercises 
2.4. Answers

3. INVERTIBLE MATRICES 
3.1. Introduction 
3.2. A method of obtaining the inverse of a square matrix 
3.3. Exercises 
3.4. Answers

4. SYSTEMS OF LINEAR EQUATIONS 
4.1. Introduction 
4.2. Cramer's theorem 
4.3. Method of matrix inversion 
4.4. Method of Gaussian elimination 
4.5. The rank of a matrix 
4.6. Fundamental theorem for systems of linear equations 
4.7. Application of Gaussian elimination to find the inverse of a matrix 
4.8. Exercises 
4.9. Answers

5. EIGENVALUES AND EIGENVECTORS 
5.1. Introduction 
5.2. Eigenvalues and eigenvectors 
5.3. Symmetric and skew-symmetric matrices 
5.4. Useful properties 
5.5. Application to ordinary differential equations 
5.6. Case of repeated roots 
5.7. Nonhomogeneous equation. Variation of parameters 
5.8. Undetermined coefficients 
5.9. Exercises 
5.10. Answers

REFERENCES